If the ratio of the roots of the equation 4x^(2)-6x+p=0 is 1:2 then the value of p is
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Answered by
6
4×^2-6x+p=0
if x=1/2
then 4^2-6×1/2+p=0
16-3+p=0
13+p=0
p= -13
Answered by
9
Answer:
The value of 'p' = 2
Step-by-step explanation:
Given
The quadratic equation is 4x²-6x+p=0
The ratio of the roots of the equation = 1:2
To find,
The value of 'p'
Recall the formula,
If α and β are the roots of the quadratic equation ax² + bx +c = 0, then
α + β = and αβ =
Solution:
Since the roots of the quadratic equation are in the ratio 1:2, let the take the roots as 'k' and '2k'
Comparing the given equation with ax² + bx +c = 0, we get
a = 4, b = -6 and c = p
Since the roots are k and 2k we have, α = k and β = 2k
α + β = ⇒k+2k =
⇒3k =
⇒k =
Also we have,
αβ = ⇒k×2k =
2k²=
Substitute the value of k = we get,
2( )² =
2× =
p = 2
∴ The value of 'p' = 2
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